All Questions

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This question is about semigroup theory. Let $E$ be a locally compact metric space, and $X=(X_t,t\ge 0;\,P_x,x\in E)$ be a Markov process on $E$. We assume that $X$ is symmetric with respect to $m$, ...

I have a question about semigroups of one-dimensional diffusions. Let $X$ be the Ornstein-Uhlenbeck process on $\mathbb{R}$. The generator is expresses as $$\frac{d^2}{dx^2}-x\frac{d}{dx}.$$ It is ...

I have a question about the following definition: A probability measure $\mu$, such that the Markov semigroup $e^{Lt} \in \mathcal{L}(L^2)$ exists and is symmetric, satisfies the Sobolev inequality ...

In Lamperti's Stochastic Processes, given a time-homogeneous Markov process $X(t), t\geq 0$ with Markov transition kernel $p_t(x,E)$ and state space being a measurable space $(S, \mathcal{F})$, a ...